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The easiest way is through prime factorization.
Example: 1/30 and 1/42
The lowest common denominator in this case is the LCM of 30 and 42.
2 x 3 x 5 = 30
2 x 3 x 7 = 42
2 x 3 x 5 x 7 = 210, the LCM and the lowest common denominator.
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